Asymptotic behavior of exotic Lagrangian tori T-a,T-b,T-c in CP2 as a plus b plus c -> infinity
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- Title
- Asymptotic behavior of exotic Lagrangian tori T-a,T-b,T-c in CP2 as a plus b plus c -> infinity
- Authors
- Lee, Weonmo; Oh, Yong-Geun; Vianna, Renato
- Date Issued
- 2021-07
- Publisher
- INT PRESS BOSTON, INC
- Abstract
- In this paper, we study various asymptotic behavior of the infinite family of monotone Lagrangian tori T-a,T-b,T-c in CP2 associated to Markov triples (a, b, c) described in [Via16]. We first prove that the Gromov capacity of the complement CP2\T-a,T-b,T-c is greater than or equal to 1/3 of the area of the complex line for all Markov triple (a, b, c). We then prove that there is a representative of the family {T-a,T-b,T-c} whose loci completely miss a metric ball of nonzero size and in particular the loci of the union of the family is not dense in CP2.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/113109
- DOI
- 10.4310/JSG.2021.v19.n3.a4
- ISSN
- 1527-5256
- Article Type
- Article
- Citation
- JOURNAL OF SYMPLECTIC GEOMETRY, vol. 19, no. 3, page. 607 - 634, 2021-07
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